Field of the Invention
The present invention relates to a calculation method, storage medium, information processing apparatus, and measurement apparatus.
Description of the Related Art
As a measurement apparatus for accurately measuring the three-dimensional shape of a measurement object such as an optical element or mold, Japanese Patent No. 3272952 has proposed a scanning type measurement apparatus which obtains shape data of a measurement object by scanning a measurement probe on the measurement object. That is, Japanese Patent No. 3272952 has disclosed a measurement apparatus which brings a measurement probe into contact with a measurement target surface, detects a reaction force at the contact point, and scans the measurement probe along the measurement target surface while controlling the reaction force to a predetermined value, thereby rapidly obtaining shape data of the measurement target surface at a high resolution.
When scanning the measurement probe in contact with the measurement target surface, the following two problems arise.
(1) A friction force is generated at the contact point, and this causes an error with respect to a contact force to be controlled.
(2) The contact force displaces the measurement target surface, and this causes an error with respect to the contact point.
These problems become serious especially when the measurement target surface partially or entirely has an inclination angle with respect to the scanning direction of the measurement probe.
Due to these error factors, shape data of the measurement target surface contains a measurement error which changes in accordance with the scanning direction of the measurement probe. This means that, for example, when the scanning pattern of the measurement probe is a raster pattern, as shown in FIG. 15, a discontinuous stepped error significantly occurs between adjacent shape data (data lines). This stepped error can be regarded as a shape error of a high-order spatial frequency component which appears depending on the scanning pitch of the measurement probe. Therefore, an averaging process or weighted averaging process can be performed on adjacent shape data, but these processes decrease the resolution of shape data of the whole measurement target surface.
Japanese Patent Laid-Open Nos. 2012-168001 and 2005-156235 have proposed techniques for solving the problems concerning the inclination and friction of the measurement target surface when scanning the measurement probe. Japanese Patent Laid-Open No. 2012-168001 has disclosed a measurement apparatus including a driving mechanism which drives a measurement probe in the Z-axis direction. This measurement apparatus detects a force generated on the measurement probe in the X-axis direction when scanning the measurement probe on an inclined surface, and, if this force exceeds a threshold value, reduces a change in contact force by driving the measurement probe in the Z-axis direction.
Also, the force generated on the measurement probe in the X-axis direction when scanning the measurement probe downward along the inclined surface is smaller than that when scanning the measurement probe upward along the inclined surface. Therefore, Japanese Patent Laid-Open No 2005-156235 has disclosed a measurement method of accurately obtaining the shape of a measurement target surface by adopting only shape data obtained when the X-axis-direction force which causes a measurement error is small, that is, obtained when scanning the measurement probe downward along an inclined surface.
Unfortunately, the measurement apparatus disclosed in Japanese Patent Laid-Open No. 2012-168001 requires a detection mechanism for detecting the X-axis-direction force generated on the measurement probe, and a driving mechanism for driving the measurement probe in the Z-axis direction. These mechanisms complicate the apparatus configuration and increase the weight of the measurement probe. Accordingly, it is unrealistic to construct the measurement apparatus as disclosed in Japanese Patent Laid-Open No. 2012-168001.
Also, the measurement method disclosed in Japanese Patent Laid-Open No. 2005-156235 does not adopt shape data obtained when scanning the measurement probe upward along an inclined surface. This decreases the resolution of shape data of the whole measurement target surface to about ½. To suppress this decrease in resolution, it is necessary to, for example, scan the measurement probe twice for one data line. This doubles the time required to measure the shape of the measurement target surface.